11.15 Suppose two independent renewal processes are denoted with N1(t) and N2(t). Assume that each inter-arrival time for both processes has the same distribution F(x) and density f(x) exists.

a) Is the process N1(t) + N2(t) a renewal process? Explain.

b) Let Y(t) denote the time until the first arrival after time t from either of the two processes. Find an expression for the distribution function of Y(t) as t → ∞.